Temperature distributions in end caps of cylindrical reactor fuel elements

The temperature distributions in bonded end caps of solid cylindrical reactor fuel elements with an internal, uniform heat source are determined theoretically. The solution for the temperature distributions is expressed by products of Bessel functions with hyperbolic functions. An illustrative example is chosen for enriched uranium oxide fuel elements with zircaloy cladding and bonded zircaloy end caps. The lengths of the end caps are 0.5, 1.0 and 1.5 times the fuel-rod radius. The results of the example indicate that relatively long end caps have somewhat lower maximum temperatures and lower radial temperature gradients than short end caps. These maximum temperatures and radial temperature gradients tend to approach constants as the lengths of the end caps increase. The maximum surface temperature of the end caps is checked against the corrosion temperature limit of zircaloy in water coolant of nuclear reactors.